Proof step e-33dba7e79fe9caa8

basis_map A008288 → concludes about delannoy JSON

Theorem

Affine-current basis map theorem polytool RealRooted orderTwoConstants_nonneg_iff ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A008288",
  "operation": "basis_map"
}

Premises

• a(n) = 1 if n is of the form m(m+3)/2, otherwise 0. (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in [0, 0]

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "lower": { "closed": true, "exact": { "radicand": "2", "rational_part": "-3", "sqrt_coefficient": "-2" }, "value": "-1564556493/268435456" }, "upper": { "closed": true, "exact": { "radicand": "2", "rational_part": "-3", "sqrt_coefficient": "2" }, "value": "-46056243/268435456" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 efd569ebbe7b8719c045da9b1b2f9612dcbf2177429b29c9c4a3a11adc84c14b, 14,489 bytes (2,260 compressed); download JSON

Cited by

• n-e00a1cb428776eaa (one_signed_coefficients)
• n-e00a1cb428776eaa (hadamard_kernel)
• n-e00a1cb428776eaa (real_rooted)